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Math Help - The Conical Pendulum

  1. #1
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    The Conical Pendulum

    I'm stuck on this question:

    A light inextensible string AB of length 3l has its ends fixed to two points A and B which are in a vertical line with A a distance l above B. A smooth ring of mass m is threaded on the string and is made to move in a horizontal circle centre B with a constant speed. Calculate the tension in he string and the speed of the ring.

    When I tried to calculate th tension I found that I needed either the radius of the circle of the diatance from either A or B to the ring, which I don't have. Have I missed something in the question? Could someone help please?
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  2. #2
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    Quote Originally Posted by free_to_fly View Post
    I'm stuck on this question:

    A light inextensible string AB of length 3l has its ends fixed to two points A and B which are in a vertical line with A a distance l above B. A smooth ring of mass m is threaded on the string and is made to move in a horizontal circle centre B with a constant speed. Calculate the tension in he string and the speed of the ring.

    ...
    I've attached a sketch of the situation as I understand it.

    If I'm right the string forms a right triangle where the sides x and y have the length 3l:

    x+y = 3l ....... [1]

    y^2 + l^2 = x^2....... [2]

    From [1] you get: y = 3l - x . Substitute this term into [2]:

    (3l-x)^2 + l^2 = x^2~\iff~ 10l^2 = 6lx~\iff~ x=\frac53 \cdot l

    That means y = \frac43 \cdot l which is the radius of the circle.
    Attached Thumbnails Attached Thumbnails The Conical Pendulum-rotier_ring.gif  
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